Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
274 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #2075 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C2×#41×C59 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ C2×#131×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#2161 | C2 | semidirect |
| 5. C59×#1388 | C2 | semidirect |
| 6. C59×#1383 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 115. #13497 | C59 | direct (N × H) |
| 128. #2161 | C2×C59 | semidirect |
| 132. #1388 | C2×C59 | semidirect |
| 133. #1383 | C2×C59 | semidirect |
| 134. #1383 | C2×C59 | semidirect |
| 153. C59 | #13497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2161 | 2 |
| C59×#2117 | 2 |
| C59×#1815 | 2 |
| C59×#1813 | 2 |
| C59×#1388 | 2 |
| C59×#1383 | 2 |
| #13497 | 59 |